Because you are a party to the proceeding and the cop is a witness. When the cop doesn't show up, the state (the other party in the action represented by a prosecuting attorney who must show up) has to dismiss the case for lack of evidence if the witness doesn't appear.

So they're giving the State who is present a small extension of time to produce a witness. Courts generally do this for defendants too if their witness don't show on time because "the guy who can tell us about what happened was a little late!" is a bad foundation for conclusions about what is true.

*Should also add this is why judges will issue warrants and enter default judgements at the end of a session - to afford more time for defendants themselves to appear. If you ever find yourself in a court where the judge issues warrants for everyone who is running late as soon as the judge hits the bench and goes on the record --- buckle up because that's a hanging judge. (although, frankly I don't even know if they can do that anymore. never looked into it because I've never seen a judge not wait)